refactor: Move dual nonlinear solving to NonlinearSolveBase (#513) #1881

Job	Run time
ModelingToolkit.jl/All/1	1h 33m 18s
OrdinaryDiffEq.jl/Interface/1	6h 0m 8s
OrdinaryDiffEq.jl/Regression/1	37m 59s
BoundaryValueDiffEq.jl/All/1	31m 42s
DiffEqCallbacks.jl/All/1	29m 26s
	9h 12m 33s

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